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Topological Characterization of Haze Episodes Using Persistent Homology

Category: Air Pollution Modeling

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DOI: 10.4209/aaqr.2018.08.0315

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Nur Fariha Syaqina Zulkepli , Mohd Salmi Md Noorani, Fatimah Abdul Razak, Munira Ismail, Mohd Almie Alias

  • School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia


  • Topological features of particulate matter are extracted using persistent homology.
  • Diverse pattern of topological features distinguish months with and without haze.
  • Summary statistics were calculated to summarize topological features.
  • Drastic changes of topological features were observed during haze episodes.


Haze phenomenon is one of the major environmental issues that have continuously vexed countries worldwide, including Malaysia, for the last three decades. Therefore, this study aims to investigate the differences between topological features of months with and without haze episodes at air quality monitoring stations located in the areas of Jerantut, Klang, Petaling Jaya, and Shah Alam. This is achieved by opting for persistent homology, which is a method in topological data analysis (TDA) that analyses data in a qualitative (topological) sense via a focus on topological features, such as connected components and holes of the data. Topological features from particulate matter (PM10) data with summary statistics are subsequently utilized to summarize them. The results have consequently shown drastic changes present in the summary statistics of the lifetimes of topological features during haze episodes. These characteristics have been consistently observed in each air quality monitoring station involved in this study. Thus, this finding highlights the potential application for the development of an early warning system for haze detection based on the topological approach.


Haze Particulate matter Persistent homology Time delay embedding Topological data analysis

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